Length-to-diameter

Extmsion accounts for about 30% of nylon produced and is used in various processes (24). Nylons can be extmded on conventional equipment having the following characteristics. The extmder drive should be capable of continuous variation over a range of screw speeds. Nylon often requires a high torque at low screw speeds typical power requirements would be a 7.5-kW motor for a 30-mm machine or 25-kW for 60-mm. A nylon screw is necessary and should not be cooled. Recommended compression ratios ate between 3.5 1 and 4 1 for nylon-6,6 and nylon-6 between 3 1 and 3.5 1 for nylon-11 and nylon-12. The length-to-diameter ratio, T/D should be greater than 15 1 at least 20 1 is recommended for nylon-6,6, and 25 1 for nylon-12. 

A combination of tapered shaft diameter and increasing pitch is shown in Figure 10a. This allows a length-to-diameter ratio of about 6 1 instead of 3 1. A half pitch screw is used over the tapered diameter. This approach results in an exceUent mass flow pattern provided that the hopper to which it attaches is also designed for mass flow. 

These design fundamentals result in the requirement that space velocity, effective space—time, fraction of bubble gas exchanged with the emulsion gas, bubble residence time, bed expansion relative to settled bed height, and length-to-diameter ratio be held constant. Effective space—time, the product of bubble residence time and fraction of bubble gas exchanged, accounts for the reduction in gas residence time because of the rapid ascent of bubbles, and thereby for the lower conversions compared with a fixed bed with equal gas flow rates and catalyst weights. 

Viscous Transport. Low velocity viscous laminar dow ia gas pipes is commonplace. Practical gas dow can be based on pressure drops of <50% for low velocity laminar dow ia pipes whose length-to-diameter ratio may be as high as several thousand. Under laminar dow, bends and fittings add to the frictional loss, as do abmpt transitions. 

FIG. 5-2 Heating and cooling of a solid cylinder having an infinite ratio of length to diameter. 

The dimensionless relations are usually indicated in either of two forms, each yielding identical resiilts. The preferred form is that suggested by Colburn ran.s. Am. In.st. Chem. Eng., 29, 174—210 (1933)]. It relates, primarily, three dimensionless groups the Stanton number h/cQ, the Prandtl number c Jk, and the Reynolds number DG/[L. For more accurate correlation of data (at Reynolds number <10,000), two additional dimensionless groups are used ratio of length to diameter L/D and ratio of viscosity at wall (or surface) temperature to viscosity at bulk temperature. Colburn showed that the product of the Stanton number and the two-thirds power of the Prandtl number (and, in addition, power functions of L/D and for Reynolds number <10,000) is approximately equal to half of the Fanning friction fac tor//2. This produc t is called the Colburn j factor. Since the Colburn type of equation relates heat transfer and fluid friction, it has greater utility than other expressions for the heat-transfer coefficient. 

The drag coefficients for disks (flat side perpendicular to the direction of motion) and for cylinders (infinite length with axis perpendicular to the direclion of motion) are given in Fig. 6-57 as a Function of Reynolds number. The effect of length-to-diameter ratio for cylinders in the Newton s law region is reported by Knudsen and Katz Fluid Mechanics and Heat Transfer, McGraw-Hill, New York, 1958). 

External-pressure failure of shells can result from overstress at one extreme or n om elastic instability at the other or at some intermediate loading. The code provides the solution for most shells by using a number of charts. One chart is used for cylinders where the shell diameter-to-thickness ratio and the length-to-diameter ratio are the variables. The rest of the charts depic t curves relating the geometry of cyhnders and spheres to allowable stress by cui ves which are determined from the modulus of elasticity, tangent modulus, and yield strength at temperatures for various materials or classes of materials. The text of this subsection explains how the allowable stress is determined from the charts for cylinders, spheres, and hemispherical, ellipsoidal, torispherical, and conical heads. 

Frequently cost savings for cylindrical shells can result from reducing the effective length-to-diameter ratio and thereby reducing shell thickness. This can be accomplished by adding circumferential stiffeners to the shell. Rules are included for designing and locating the stiffeners. 

Rotaiy wheel atomizers require 0.8 to 1.0 kWh/1,000 L. The lateral throw of a spray wheel requires a large diameter to prevent accumulation on the wall length to diameter ratios of 0.5 to 1.0 are in use in such cases. The downward throw of spray nozzles permits smaller diameters but greater depths L/D ratios of 4 to 5 or more are used. Spray vessel diameters of 15 m (50 ft) or more are known. The technology of spray drying is apphcable. 

Length-to-diameter ratio of vessel Static activation overpressure Ps,ai of venting device... 

Mixing of product and feed (backmixing) in laboratory continuous flow reactors can only be avoided at very high length-to-diameter (aspect) ratios. This was observed by Bodenstein and Wohlgast (1908). Besides noticing this, the authors also derived the mathematical expression for reaction rate for the case of complete mixing. 

Length. Combustor length must be sufficient to provide for flame stabilization, combustion, and mixing with dilution air. The typical value of the length-to-diameter ratio for liners ranges from three to six. Ratios for casing range from two to four. 

Another important advantage of the tilting-pad journal bearing is its ability to aeeommodate shaft misalignment. Beeause of its relatively short length-to-diameter ratio, it ean aeeommodate minor misalignment quite easily. 

Assign a length-to-diameter ratio of 5, and size a tank to accommodate the required holdup time. 

Heat Exchanger Approach 5°C = 40°F Approx Friction Factor 0.005 (1 velocity head loss every 50-60 length to diameter ratios)... 

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